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Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data

Junya Otsuki, Masayuki Ohzeki, Hiroshi Shinaoka, and Kazuyoshi Yoshimi
Phys. Rev. E 95, 061302(R) – Published 21 June 2017

Abstract

A data-science approach to solving the ill-conditioned inverse problem for analytical continuation is proposed. The root of the problem lies in the fact that even tiny noise of imaginary-time input data has a serious impact on the inferred real-frequency spectra. By means of a modern regularization technique, we eliminate redundant degrees of freedom that essentially carry the noise, leaving only relevant information unaffected by the noise. The resultant spectrum is represented with minimal bases and thus a stable analytical continuation is achieved. This framework further provides a tool for analyzing to what extent the Monte Carlo data need to be accurate to resolve details of an expected spectral function.

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  • Received 15 February 2017

DOI:https://doi.org/10.1103/PhysRevE.95.061302

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Junya Otsuki1, Masayuki Ohzeki2, Hiroshi Shinaoka3, and Kazuyoshi Yoshimi4

  • 1Department of Physics, Tohoku University, Sendai 980-8578, Japan
  • 2Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
  • 3Department of Physics, Saitama University, Saitama 338-8570, Japan
  • 4Institute for Solid State Physics, University of Tokyo, Chiba 277-8581, Japan

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Issue

Vol. 95, Iss. 6 — June 2017

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